THE DIGITAL FORM OF OPERATORS ON BAND-LIMITED FUNCTIONS,
Abstract
Functions whose spectrum is limited to frequencies symmetrically situated with respect to zero and contained either in one interval (low-pass) or in two intervals (band-pass) can be represented faithfully by their values at equidistant points in time. If such functions are represented by a table of numbers in a computer, it is important to know by which operations on these numbers various operations of analysis are represented. The present report gives in detail the representation of differentiation, convolution, Fourier transformation and Hilbert transformation. It is shown how the latter operation is used to obtain the amplitude and phase of the band-limited function from the sampled data. The justification of the formulas is based on the theorem that every bounded operation on B, the space of band-limited functions, can be applied term by term to the Whittacker-Shannon representation of a band-limited function. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1967
- Accession Number
- AD0675811
Entities
People
- Henry P. Kramer
Organizations
- General Electric